Question

Which of the following is an example of an equation with no solution?(1 point)

Responses
1. 3x+4=3x+4
2. 3x+4=4x+3
3. 3x+4=3x+3
4. 4x+3=3x+3
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 1

Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
1. 4x+3=4x+3
2. 3x+4=3x+4
3. 3x+4=3x+3
4. 3x+4=4x+3
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 2

Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x (1 point)

Responses
1. The equation has infinite solutions.
2. The equation has no solution.
3. The equation has one solution: x=3.
4. The equation has one solution: x=−3.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 3

Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point)
Responses
1. The equation has one solution: x=0.
2. The equation has infinite solutions.
3. The equation has no solution.
4. The equation has one solution: x=−10.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 4

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)
Responses
1. The equation has one solution: x=6.
2. The equation has no solution.
3. The equation has one solution: x=10.
4. The equation has infinite solutions.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 5

Thanks Mini Bot all of these answers are right!

Answer 6

The equation with no solution is:

3. \(3x + 4 = 3x + 3\)

To explain: when you subtract \(3x\) from both sides, you get \(4 = 3\), which is a false statement and indicates that there is no solution.

Answer 7

The equation with exactly one solution is:

**4. \(3x + 4 = 4x + 3\)**

To explain: When you solve this equation, you move the terms involving \(x\) to one side and the constants to the other:

1. Subtract \(3x\) from both sides: \(4 = x + 3\)
2. Subtract \(3\) from both sides: \(1 = x\)

This gives you a single solution, \(x = 1\). The other options either have no solution or infinitely many solutions.

Answer 8

Let's solve the equation \(3(x + 2) - 6 = 3x\).

1. Distribute on the left side:
\[
3x + 6 - 6 = 3x
\]
This simplifies to:
\[
3x = 3x
\]

At this point, since both sides of the equation are the same, this means that the equation holds true for all values of \(x\).

Thus, the equation has **infinite solutions**.

The correct answer is:
**1. The equation has infinite solutions.**

Answer 9

Let's solve the equation \(4x = 3(x + 5) - 15\).

1. Distribute the \(3\) on the right side:
\[
4x = 3x + 15 - 15
\]
This simplifies to:
\[
4x = 3x
\]

2. Subtract \(3x\) from both sides:
\[
4x - 3x = 0
\]
This gives:
\[
x = 0
\]

Since we have found a specific solution for \(x\), the equation has **one solution.**

The correct answer is:
**1. The equation has one solution: x=0.**

Answer 10

Let's solve the equation \(5(2x + 2) - 7x = 3x + 6\).

1. Distribute the \(5\) on the left side:
\[
10x + 10 - 7x = 3x + 6
\]
This simplifies to:
\[
3x + 10 = 3x + 6
\]

2. Now, subtract \(3x\) from both sides:
\[
10 = 6
\]

This results in a false statement, which indicates that there are **no solutions** to the equation.

The correct answer is:
**2. The equation has no solution.**

Answer 11

You're welcome! I'm glad to hear that the answers were helpful. If you have any more questions or need further assistance, feel free to ask!